Simplify 2/(x(x + 4)) - 1/(x + 4) Step by Step

Step by step

The question

Question: work out 2/x(x + 4) − 1/(x + 4).

2x(x + 4) − 1x + 4

1 Find the common bottom

The bottoms are x(x + 4) and (x + 4).

bottoms: x(x + 4) and (x + 4)

The common bottom must have every factor of both bottoms, each one once.

It is x(x + 4).

common bottom = x(x + 4)

Careful!

We can't take away the tops and take away the bottoms.

Fractions need the same bottom first.

Careful: not 1x² + 3x − 4 ✗

2 Make the bottoms the same

The first fraction already has it.

The second fraction is missing x.

We multiply its top and bottom by x.

x/x is 1, so the value stays the same.

= 2x(x + 4) − x(x + 4)x

3 Take away the tops

Now one fraction: (2 − x)/x(x + 4).

= 2 − xx(x + 4)

On top: 2 − x is −x + 2.

2 − x = −x + 2

So the top is −x + 2.

= −x + 2x(x + 4)

4 Cross out the same

Is a whole factor on top the same as one on the bottom?

No.

So nothing crosses out.

We leave the bottom as factors.

So the answer is (−x + 2)/x(x + 4).

The bottoms can't be 0.

So x can't be −4 or 0.

x ≠ −4, 0

5 Check

Let's check with a number: x = 1.

First in the question.

2/5 take away 1/5 is 1/5.

Question: 21(1 + 4) − 11 + 4 = 25 − 15 = 15

Now in our answer.

We get 1/5 too.

Answer: −1 + 21(1 + 4) = 15

Both are 1/5.

So (−x + 2)/x(x + 4) is right!

Let's look back.

First: find the common bottom.

Then: make the bottoms the same.

Then: take away the tops.

Then: cross out the same.

Last: check.

Answer